Fast GPU-based computation of the sensitivity matrix for a PET list-mode OSEM algorithm

During the last decade, studies have shown that 3D list-mode ordered-subset expectation-maximization (LM-OSEM) algorithms for positron emission tomography (PET) reconstruction could be effectively computed and considerably accelerated by graphics processing unit (GPU) devices. However, most of these studies rely on pre-calculated sensitivity matrices. In many cases, the time required to compute this matrix can be longer than the reconstruction time itself. In fact, the relatively long time required for the calculation of the patient-specific sensitivity matrix is considered as one of the main obstacle in introducing a list-mode PET reconstruction algorithm for routine clinical use. The objective of this work is to accelerate a fully 3D LM-OSEM algorithm, including the calculation of the sensitivity matrix that accounts for the patient-specific attenuation and normalization corrections. For this purpose, sensitivity matrix calculations and list-mode OSEM reconstructions were implemented on GPUs, using the geometry of a commercial PET system. The system matrices were built on-the-fly by using an approach with multiple rays per detector pair. The reconstructions were performed for a volume of 188x188x57 voxels of 2x2x3.15 mm(3) and for another volume of 144x144x57 voxels of 4x4x3.15 mm(3). The time to compute the sensitivity matrix for the 188x188x57 array was 9 s while the LM-OSEM algorithm performed at a rate of 1.1 millions of events per second. For the 144x144x57 array, the respective numbers are 8 s for the sensitivity matrix and 0.8 million of events per second for the LM-OSEM step. This work lets envision fast reconstructions for advanced PET applications such as real time dynamic studies and parametric image reconstructions.